Method for the efficiency-corrected real-time quantification of nucleic acids

ABSTRACT

The present invention concerns a method for the quantification of a target nucleic acid in a sample comprising the following steps: (i) determination of the amplification efficiency of the target nucleic acid under defined amplification conditions, (ii) amplification of the target nucleic acid contained in the sample under the same defined reaction conditions, (iii) measuring the amplification in real-time, (iv) quantification of the original amount of target nucleic acid in the sample by correction of the original amount derived from step (iii) with the aid of the determined amplification efficiency. The efficiency correction of PCR reactions according to the invention for the quantification of nucleic acids can be used for absolute quantification with the aid of an external or internal standard as well as for relative quantification compared to the expression of housekeeping genes.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.10/746,993, filed Dec. 24, 2003, which is a continuation of U.S. patentapplication Ser. No. 09/823,711, filed Mar. 30, 2001, now U.S. Pat. No.6,691,041, which claims benefit of priority from European ApplicationNo. 00107036.6, filed Mar. 31, 2000 and from German Application No.10034209.4, filed Jul. 13, 2000; the disclosures of each are hereinincorporated by reference in their entirety for all purposes.

FIELD OF THE INVENTION

The present invention relates to the field of nucleic acidquantification with the aid of quantitative real-time PCR.

BACKGROUND OF THE INVENTION

Methods for the quantification of nucleic acids are important in manyareas of molecular biology and in particular for molecular diagnostics.At the DNA level such methods are used for example to determine the copynumbers of gene sequences amplified in the genome. However, methods forthe quantification of nucleic acids are used especially in connectionwith the determination of mRNA quantities since this is usually ameasure for the expression of the respective coding gene.

If a sufficient amount of sample material is available, special mRNAscan be quantified by conventional methods such as Northern Blot analysisor RNAse protection assay methods. However, these methods are notsensitive enough for sample material that is only available in smallamounts or for genes that are expressed very weakly.

The so-called RT-PCR is a much more sensitive method. In this method asingle-stranded cDNA is firstly produced from the mRNA to be analysedusing a reverse transcriptase. Subsequently a double-stranded DNAamplification product is generated with the aid of PCR.

A distinction is made between two different variants of this method:

-   -   In the so-called relative quantification the ratio of the        expression of a certain target RNA is determined relative to the        amount of RNA of a so-called housekeeping gene which is assumed        to be constitutively expressed in all cells independent of the        respective physiological status. Hence the mRNA is present in        approximately the same amount in all cells.

The advantage of this is that different initial qualities of the varioussample materials and the process of RNA preparation has no influence onthe particular result. However, an absolute quantification is notpossible with this method.

-   -   Alternatively the absolute amount of RNA used can be determined        with the aid of standard nucleic acids of a known copy number        and amplification of a corresponding dilution series of this        standard nucleic acid. There are two alternatives:

When using external standards the standard and target nucleic acid areamplified in separate reaction vessels. In this case a standard can beused with an identical sequence to the target nucleic acid. However,systematic errors can occur in this type of quantification if the RNApreparation to be analysed contains inhibitory components which impairthe efficiency of the subsequent PCR reaction. Such errors can beexcluded by using internal standards i.e. by amplifying the standard andtarget nucleic acid in one reaction vessel. However, a disadvantage ofthis method is that standards have to be used that have differentsequences compared to the target nucleic acid to be analysed in order tobe able to distinguish between the amplification of the standard andtarget nucleic acid. This can in turn lead to a systematic error in thequantification since different efficiencies of the PCR amplificationcannot be excluded when the sequences are different.

PCR products can be quantified in two fundamentally different ways:

a) End Point Determination of the Amount of PCR Product Formed in thePlateau Phase of the Amplification Reaction

In this case the amount of PCR product formed does not correlate withthe amount of the initial copy number since the amplification of nucleicacids at the end of the reaction is no longer exponential and instead asaturation is reached. Consequently different initial copy numbersexhibit identical amounts of PCR product formed. Therefore thecompetitive PCR or competitive RT-PCR method is usually used in thisprocedure. In these methods the specific target sequence is coamplifiedtogether with a dilution series of an internal standard of a known copynumber. The initial copy number of the target sequence is extrapolatedfrom the mixture containing an identical PCR product quantity ofstandard and target sequence (Zimmermann and Mannhalter, Bio-Techniques21:280-279, 1996). A disadvantage of this method is also thatmeasurement occurs in the saturation region of the amplificationreaction.

b) Kinetic Real-Time Quantification in the Exponential Phase of PCR.

In this case the formation of PCR products is monitored in each cycle ofthe PCR. The amplification is usually measured in thermocyclers whichhave additional devices for measuring fluorescence signals during theamplification reaction. A typical example of this is the RocheDiagnostics LightCycler (Cat. No. 2 0110468). The amplification productsare for example detected by means of fluorescent labelled hybridizationprobes which only emit fluorescence signals when they are bound to thetarget nucleic acid or in certain cases also by means of fluorescentdyes that bind to double-stranded DNA. A defined signal threshold isdetermined for all reactions to be analysed and the number of cycles Cprequired to reach this threshold value is determined for the targetnucleic acid as well as for the reference nucleic acids such as thestandard or housekeeping gene. The absolute or relative copy numbers ofthe target molecule can be determined on the basis of the Cp valuesobtained for the target nucleic acid and the reference nucleic acid(Gibson et al., Genome Research 6:995-1001; Bieche et al., CancerResearch 59:2759-2765, 1999; WO 97/46707; WO 97/46712; WO 97/46714).

In summary in all the described methods for the quantification of anucleic acid by PCR the copy number formed during the amplificationreaction is always related to the copy number formed of a referencenucleic acid which is either a standard or an RNA of a housekeepinggene. In this connection it is assumed that the PCR efficiency of thetarget and reference nucleic acid are not different.

Usually a PCR efficiency of 2.00 is assumed which corresponds to adoubling of the copy number per PCR cycle (User Bulletin No. 2 ABI Prism7700, PE Applied Biosystems, 1997).

However, it has turned out that the real PCR efficiency can be differentfrom 2.00 since it is influenced by various factors such as the bindingof primers, length of the PCR product, G/C content and secondarystructures of the nucleic acid to be amplified and inhibitors that maybe present in the reaction mixture as a result of the samplepreparation. This is particularly relevant when using heterologousreference nucleic acids e.g. in the relative quantification compared tothe expression of housekeeping genes.

SUMMARY OF THE INVENTION

The object of the present invention was therefore to provide methods forthe quantification of nucleic acids which overcome the disadvantages ofthe prior art as described above. The object of the present inventionwas in particular to provide methods for the quantification of nucleicacids in which a target nucleic acid is quantified independent of theamplification efficiencies of target nucleic acid and reference nucleicacid.

This object is achieved according to the invention by a method for thequantification of a target nucleic acid in a sample comprising thefollowing steps:

-   a) Determining the amplification efficiency of the target nucleic    acid under defined conditions.-   b) Amplifying the target nucleic acid contained in the sample under    the same reaction conditions.-   c) Measuring the amplification in real-time.-   d) Quantifying the original amount of target nucleic acid in the    sample by correction of the original amount derived from step c)    with the aid of the determined amplification efficiency.

According to the invention this method can be used for relativequantification compared to the expression of housekeeping genes as wellas for absolute quantification.

A first aspect of the invention therefore concerns a method forquantifying a target nucleic acid in a sample compared to a referencenucleic acid comprising the following steps:

-   a) Determining the amplification efficiencies of the target nucleic    acid and reference nucleic acid under defined amplification    conditions-   b) Amplifying the target nucleic acid contained in the sample as    well as the reference nucleic acid contained in the sample under the    same defined amplification conditions.-   c) Measuring the amplification of the target nucleic acid and    reference nucleic acid in real-time-   d) Calculating the original ratio of target nucleic acid and    reference nucleic acid in the sample by correcting the ratio derived    from step c) with the aid of the amplification efficiencies    determined in step a).

A second aspect of the present invention concerns a method for thequantification of a target nucleic acid in a sample comprising thefollowing steps:

-   a) Determining the amplification efficiencies of the target nucleic    acid and of an internal or an external standard under defined    amplification conditions-   b) Amplifying the target nucleic acid contained in the sample as    well as the internal or external standard under the same defined    reaction conditions-   c) Measuring the amplification of the target nucleic acid and    standard in real-time-   d) Calculating the original copy number in the sample by correcting    the copy number derived from step c) with the aid of the    amplification efficiencies determined in step a).

In all methods the amplification efficiencies are preferably determinedby

-   a) preparing a dilution series of the target nucleic acid-   b) amplifying the target nucleic acid under defined reaction    conditions according to A, the amplification of the nucleic acids    being measured in real-time-   c) setting a defined signal threshold value-   d) determining the cycle number for each dilution at which the    signal threshold value is exceeded,-   e) calculating the amplification efficiency based on the determined    cycle numbers.

DETAILED DESCRIPTION OF THE INVENTION

The object of the invention is achieved by a method for thequantification of a target nucleic acid in a sample comprising thefollowing steps:

-   a) Determining the amplification efficiency of the target nucleic    acid under defined conditions-   b) Amplifying the target nucleic acid contained in the sample under    the same reaction conditions.-   c) Measuring the amplification in real-time-   d) Quantifying the original amount of target nucleic acid in the    sample by correcting the original amount derived from step c) with    the aid of the determined amplification efficiency.

The importance of an efficiency correction will be illustrated by anerror calculation. Table 1 shows a theoretical calculation of theaverage percentage error of the determined copy number in the case ofamplification efficiencies that are different from 2.00 as a function ofthe respective cycle number.

The error is calculated according to the formulapercentage error=(2^(n) /E ^(n)−1)×100in which E is the efficiency of the amplification and n is therespective cycle number at which the percentage error is determined.

TABLE 1 Detection Cycle (n) PCR efficiency (E) 10 15 20 25 30 35 2.00 —— — — — — 1.97 16% 25% 35%  46%    57%  70% 1.95 29% 46% 66%  88%   113%142% 1.90 67% 116% 179%  260%   365% 500% 1.80 187% 385% 722% 1290%  2260% 3900%  1.70 408% 1045% 2480% 5710% 13.000% 29.500%   1.60 920%2740% 8570% 26.400%   80.700% 246.400%   

The amplification efficiency can be determined by various methods forexample by determining a function with which the measured signal isdetermined relative to the amplification of the target nucleic acid as afunction of the cycle time.

The amplification efficiency is preferably determined by a method inwhich

-   a) a dilution series of a target nucleic acid is prepared-   b) the target nucleic acid is amplified under defined reaction    conditions as claimed in claim 1 and the amplification of the    nucleic acid is measured in real-time-   c) a defined signal threshold value is set-   d) for each dilution the cycle number Cp is determined at which the    signal threshold value is exceeded-   e) a logarithmic linear function of the copy number of target    nucleic acid used for the amplification is determined as a function    of the cycle number at which the signal threshold value is exceeded-   f) the amplification efficiency E is calculated according to    E=G^(−a)    -   wherein a is determined as the first derivative of the function        determined in step e) and G is the base number of the logarithm.

In a similar manner the amplification efficiency can also be determinedby a method in which

-   a) a dilution series of the target nucleic acid is prepared-   b) the target nucleic acid is amplified under defined reaction    conditions as claimed in claim 1 and the amplification of the    nucleic acid is measured in real-time-   c) a defined signal threshold value is set-   d) the cycle number Cp at which the signal threshold value is    exceeded is determined for each dilution-   e) a linear function of the cycle number determined in step d) is    determined as a function of a logarithm of the copy number of target    nucleic acid used for the amplification and-   f) the amplification efficiency E is calculated according to    E=G ^(−1/a)    -   wherein a is determined as the first derivative of the function        determined in step e) and G is the base number of the logarithm.

Both preferred procedures have the advantage that a systematic errorcannot occur that results from determining the amplification efficiencyin a phase of the PCR reaction in which there is no longer anexponential amplification of the target nucleic acid (plateau phase).

However, it unexpectedly turned out that under certain conditions theamplification efficiency can also be dependent on the original amount oftarget nucleic acid or it can change during the first cycles of anamplification reaction that is still in the exponential phase. A subjectmatter of the invention is thus also a method for theefficiency-corrected quantification of nucleic acids in which theefficiency of the amplification is determined by

-   -   a) preparing a dilution series of the target nucleic acid    -   b) amplifying the target nucleic acid under defined reaction        conditions as claimed in claim 1 and measuring the amplification        of the nucleic acid in real-time    -   c) setting a defined signal threshold value    -   d) determining the cycle number Cp at which the signal threshold        value is exceeded for each dilution    -   e) determining the amplification efficiency as a function of the        amount of target nucleic acid.

This can for example be achieved by derivation of a continuouslydifferentiable function F(Cp) of the Cp values as a function of theoriginal copy number or vice versa.

The function F(Cp)=log(concentration of the original copy number) canfor example be standardized by mathematical algorithms such as apolynomial fit of a higher degree. The amplification efficiency E canthen be determined by the equationE=G ^(−dF(Cp)/dCp)in which dF/(Cp) is the derivative of the continuous function and G isthe base number of the logarithm. A polynomial fit of the 4^(th) degreehas proven to be particularly suitable within the sense of theinvention.

The efficiency-corrected quantification of nucleic acids according tothe invention can in principle be used for methods for absolutequantification as well as for methods for relative quantification.

Hence a subject matter of the present invention in relation to relativequantification is also a method for the quantification of a targetnucleic acid in a sample relative to a reference nucleic acid comprisingthe following steps:

-   -   a) Determination of the amplification efficiencies of the target        nucleic acid and of the reference nucleic acid under defined        amplification conditions.    -   b) Amplification of the target nucleic acid contained in the        sample as well as of the reference nucleic acid contained in the        sample under the same defined amplification conditions.    -   c) Measurement of the amplification of the target nucleic acid        and of the reference nucleic acid in real-time.    -   d) Calculation of the original ratio of target nucleic acid and        reference nucleic acid in the sample by correcting the ratio        derived from step c) with the aid of the amplification        efficiencies determined in step a).

Such a method according to the invention eliminates on the one hand theinfluence of inhibitors that may be present in the examined sample and,on the other hand, corrects errors which may occur as a result ofdifferent amplification efficiencies of the target nucleic acid andreference nucleic acid.

Steps b) to d) are advantageously carried out in a parallel mixturecontaining a so-called calibrator sample. The calibrator sample is asample which contains the target nucleic acid and reference nucleic acidin a defined ratio that is constant for each measurement. Subsequentlythe ratio of the quotients determined for the sample and for thecalibrator sample is determined as a measure for the original amount oftarget nucleic acid in the sample. This has the advantage that inaddition other systematic errors are eliminated that are due todifferences in the detection sensitivity of the target nucleic acid andreference nucleic acid. Such systematic errors can for example occur asa result of different hybridization properties of the hybridizationprobes or, in the case of fluorescent-labelled probes, differentexcitation efficiencies, quantum yields or coupling efficiencies of thedye to the probe. Therefore the sample to be tested and the calibratorsample must be analysed in each experiment with the same detectionagents i.e. with the same batch of fluorescent-labelled hybridizationprobes.

A special embodiment of relative quantification according to theinvention is a method for the quantification of a target nucleic acid ina sample relative to a reference nucleic acid comprising the followingsteps:

-   -   a) Determination of the amplification efficiencies of the target        nucleic acid and of the reference nucleic acid under defined        amplification conditions    -   b) Amplification of the target nucleic acid contained in the        sample and of the reference nucleic acid contained in the sample        under the same defined amplification conditions.    -   c) Measurement of the amplification of the target nucleic acid        and of the reference nucleic acid in real time.    -   d) Determination of a defined signal threshold value.    -   e) Determination of the cycle numbers at which the signal        threshold value is in each case exceeded during the        amplification of the target nucleic acid and the reference        nucleic acid.    -   f) Calculation of the original ratio of target nucleic acid and        reference nucleic acid in the sample according to the formula        N(T)₀ /N(R)₀ =E(R)^(n(R)) /E(T)^(n(T)), wherein

-   N(T)₀=the original amount of target DNA present in the sample

-   N(R)₀=the original amount of reference DNA present in the sample

-   E(R)=the amplification efficiency of the reference nucleic acid

-   n(R)=the cycle number of the reference nucleic acid measured in step    e)

-   E(T)=the amplification efficiency of the target nucleic acid

-   n(T)=the cycle number of the target nucleic acid measured in step e)

In this embodiment it is advantageous to carry out steps b), c), e) andf) with a calibrator sample in order to eliminate systematic errors dueto the detection of amplification products and subsequently the ratio ofthe quotients measured for the sample and for the calibrator sample aredetermined as a measure for the original amount of target nucleic acidin the sample.

The ratio obtained in step f) is calculated according to the inventionas follows:N(T)_(n) =N(T)₀ ×E(T)^(n(T))  (1)N(R)_(n) =N(R)₀ ×E(R)^(n(R))  (2)in which N(T)_(n)=the amount of target DNA at the signal threshold value

-   and N(R)_(n)=the amount of reference DNA at the signal threshold    value

From (1) and (2) it follows that:

$\begin{matrix}{\frac{{N(T)}_{n}}{{N(R)}_{n}} = \frac{{N(T)}_{0} \times {E(T)}^{n{(T)}}}{{N(R)}_{0} \times {E(R)}^{n{(R)}}}} & (3)\end{matrix}$From this it follows that:

$\begin{matrix}{\frac{{N(T)}_{0}}{{N(R)}_{0}} = \frac{{N(T)}_{n} \times {E(R)}^{n{(R)}}}{{N(R)}_{n} \times {E(T)}^{n{(T)}}}} & (4)\end{matrix}$

Due to the fact that an identical signal threshold value has been setfor the target and reference nucleic acid this may be approximated to:N(T)_(n) =N(R)_(n).

Under this condition and starting from equation (4) for the originalratio of target nucleic acid and reference nucleic acid, this results inthe equationN(T)₀ /N(R)₀ =E(R)^(n(R)) /E(T)^(n(T))  (5)

However, this assumed approximation does not apply when target nucleicacid and reference nucleic acid are detected with differentsensitivities. According to the invention it is therefore particularlyadvantageous to measure a calibrator sample in a parallel reaction andto determine the ratio of the quotients N(T)₀/N(R)₀ measured for thesample and for the calibrator sample as a measure for the originalamount of target nucleic acid in the sample.

This results in the following from equation (4) using the indices

_(A) for the sample to be analysed and

_(K) for the calibrator sample

$\begin{matrix}{{\frac{{N(T)}_{0A}}{{N(R)}_{0A}}/\frac{{N(T)}_{0K}}{{N(R)}_{0K}}} = \frac{\frac{{N(T)}_{nA} \times {E(R)}^{{nA}{(R)}}}{{N(R)}_{nA} \times {E(T)}^{{nA}{(T)}}}}{\frac{{N(T)}_{nK} \times {E(R)}^{{nK}{(R)}}}{{N(R)}_{nK} \times {E(T)}^{{nK}{(T)}}}}} & (6)\end{matrix}$

Due to the fact that an identical signal threshold value has been setfor the sample to be analysed and for the calibrator sample and thatidentical agents are used to detect target and reference amplicons inthe sample and in the calibrator sample, the ratio of the quotientdetermined for the sample and for the calibrator sample is as follows:

${\frac{{N(T)}_{nA}}{{N(R)}_{nA}}/\frac{{N(T)}_{nK}}{{N(R)}_{nK}}} = 1$

Hence the ratio of the quotients of the sample to be analysed and thecalibrator sample is:

$\begin{matrix}{{\frac{{N(T)}_{0A}}{{N(R)}_{0A}}/\frac{{N(T)}_{0K}}{{N(R)}_{0K}}} = {{E(R)}^{{{nA}{(R)}} - {{nK}{(R)}}}*{E(T)}^{{{nK}{(T)}} - {{nA}{(T)}}}}} & (7)\end{matrix}$

Consequently a relative value can be obtained in this manner for theoriginal copy number of target nucleic acid in the sample in whichsystematic errors due to different amplification efficiencies as well asdue to different detection sensitivities have been eliminated. The onlyrequirement for the accuracy of the determined value is the justifiedassumption that under absolutely identical buffer conditions theamplification and detection efficiencies are also identical in thevarious reaction vessels.

Requirement for all methods according to the invention for relativequantification is that the amplification efficiency of the targetnucleic acid as well as the amplification efficiency of the referencenucleic acid are determined. Both of these determinations are preferablycarried out by the methods described above by determining the cyclenumber at which a certain signal threshold value is exceeded.

In a preferred embodiment of relative quantification the sample isdivided into two aliquots and the real-time measurement of theamplification of the target nucleic acid and reference nucleic acid iscarried out in separate reaction vessels. This prevents interferencebetween the amplification reactions of the target nucleic acid and thereference nucleic acid with regard to their efficiency for example bycompetition for deoxynucleotides or Taq polymerase. Furthermore thetarget nucleic acid and reference nucleic acid can be detected with thesame detection systems, for example with the same DNA binding dye.

Alternatively the real-time measurement of the amplification of targetnucleic acid and reference nucleic acid can be carried out in one samplein the same reaction vessel using differently labelled hybridizationprobes. This is particularly advantageous when only small amounts ofsample material are available because the number of PCR reactionsrequired is halved in this manner.

If it is intended to determine the absolute amount of target nucleicacid to be detected in a sample, then the method for the quantificationof a target nucleic acid in a sample comprises the steps of:

-   -   a) Determination of the amplification efficiencies of the target        nucleic acid and of an internal or external standard under        defined amplification conditions;    -   b) Amplification of the target nucleic acid contained in the        sample as well as of the internal or external standard under the        same defined reaction conditions;    -   c) Measurement of the amplification of the target nucleic acid        and standard in real time; and    -   d) Calculation of the original copy number in the sample by        correcting the copy number derived from step c) with the aid of        the amplification efficiencies determined in step a).

The sequences of the target nucleic acid and standard nucleic acid areadvantageously substantially identical. However, when selecting thesequence for an internal standard it must be taken into account that theavailable detection system should be able to distinguish between thestandard and target nucleic acid. This can for example be achieved byusing hybridization probes with different labels for the detection ofthe target nucleic acid and internal standard. Ideally oligonucleotidesare used for this as detection probes which can be used to distinguishbetween minimal sequence differences such as point mutations.

An advantage of using an internal standard is that the inhibitorspresent in the sample also influence the amplification of the standard.Hence differences in the amplification efficiencies can be minimized.

In contrast the use of an external standard has the advantage that theamplification reactions of the target nucleic acid and standard cannotcompetitively interfere with one another with regard to theirefficiency. Moreover the amplification products of the standard andtarget nucleic acid can be detected in parallel reactions with the aidof the same detection system for example with the same hybridizationprobe. A disadvantage is possible differences in the PCR efficienciesdue to inhibitors in the sample. However, errors in the quantificationcaused by this can be eliminated by the method described in thefollowing:

In a preferred embodiment for the absolute quantification of a targetnucleic acid in a sample the method according to the invention comprisesthe following steps:

-   -   a) Determination of the amplification efficiencies of the target        nucleic acid as well as of an internal or external standard        under defined amplification conditions    -   b) Amplification of the target nucleic acid contained in the        sample as well as of the internal or external standard under the        same defined reaction conditions    -   c) Measurement of the amplification of target nucleic acid and        standard in real-time    -   d) Setting a defined signal threshold value    -   e) Determination of the cycle number during the amplification of        target nucleic acid and standard at which the signal threshold        value is exceeded    -   f) Determination of the original copy number N(T)₀ of the target        nucleic acid in the sample according to the formula        N(T)₀ =N(S)₀ *E(S)^(n(S)) /E(T)^(n(T))  (8) in which

N(S)₀=the original amount of standard used

E(S)=the amplification efficiency of the standard

n(S)=the cycle number of the standard measured in step e)

E(T)=the amplification efficiency of the standard

n(T)=the cycle number of the target nucleic acid measured in step e).

In this case like the relative quantification, the amplificationefficiencies of the target nucleic acid and the internal standard arepreferably determined as described by determining the cycle number atwhich a certain signal threshold value is exceeded.

According to the invention N(T)₀ is calculated as follows:N(T)_(n) =N(T)₀ *E(T)^(n(T))andN(S)_(n) =N(S)₀ *E(S)^(n(S))

Since an identical signal threshold value has been set for the targetand standard nucleic acid this approximates to:N(T)n=N(S)n

Hence the original copy number of target nucleic acid present in thesample is calculated according to the equationN(T)₀ =N(S)₀ *E(S)^(n(S)) /E(T)^(n(T))  (8)

The invention in particular also concerns those embodiments of thedescribed methods for the efficiency-corrected quantification of nucleicacids in which the amplification products are detected by hybridizationprobes which can be labelled with a detectable component in manydifferent ways.

A prerequisite for the efficiency-corrected determination of theoriginal amount of a target nucleic acid and for the determination ofthe amplification efficiencies per se is to define signal thresholdvalues and subsequently determine the cycle number for the respectiveamplification reaction at which a certain signal threshold value isreached. The signal threshold value can be determined according to theprior art in various ways:

According to the prior art the signal threshold value can for example bea signal which corresponds to a certain multiple of the statisticalvariance of the background signal (ABI Prism 7700 Application Manual,Perkin Elmer).

Alternatively the cycle number at which the signal threshold value isexceeded can be determined according to the so-called “fit point abovethreshold” method (LightCycler Operator's Manual, B59-B68, RocheMolecular Biochemicals, 1999).

In a further embodiment the threshold value can be determined as arelative value instead of an absolute value when, independently of theabsolute value of the signal, the course of the amplification reactionis determined as a function of the cycle number and subsequently then^(th) derivative is calculated. In this case exceeding certain extremescan be defined as exceeding a certain signal threshold value (EPApplication No. 0016523.4). Hence this method of determining thethreshold value is independent of the absolute signal strength of forexample a fluorescence signal. Thus it is particularly suitable forthose embodiments in which the target nucleic acid and reference nucleicacid are amplified in the same reaction vessel and are detected with theaid of different fluorescent labels. Methods have proven to beparticularly suitable for the efficiency-corrected quantification of PCRproducts in which the maximum of the second derivative is determined asa measure for the signal threshold value.

The hybridization probes used for the methods according to the inventionare usually single-stranded nucleic acids such as single-stranded DNA orRNA or derivatives thereof or alternatively PNAs which hybridize at theannealing temperature of the amplification reaction to the targetnucleic acid. These oligonucleotides usually have a length of 20 to 100nucleotides.

Depending on the detection format the label can be introduced on anyribose or phosphate group of the oligonucleotide. Labels at the 3′ and5′ end of the nucleic acid molecule are preferred.

The type of label must be detectable in the real-time mode of theamplification reaction. This is for example in principle also (but notonly) possible with the aid of labels that can be detected by NMR.

Methods are particularly preferred in which the amplified nucleic acidsare detected with the aid of at least one fluorescent-labelledhybridization probe.

Many test procedures are possible for this. The following threedetection formats have proven to be particularly suitable in connectionwith the present invention:

a) FRET Hybridization Probes

For this test format 2 single-stranded hybridization probes are usedsimultaneously which are complementary to adjacent sites of the samestrand of the amplified target nucleic acid. Both probes are labelledwith different fluorescent components. When excited with light of asuitable wavelength, a first component transfers the absorbed energy tothe second component according to the principle of fluorescenceresonance energy transfer such that a fluorescence emission of thesecond component can be measured when both hybridization probes bind toadjacent positions of the target molecule to be detected.

Alternatively it is possible to use a fluorescent-labelled primer andonly one labelled oligonucleotide probe (Bernard et al., AnalyticalBiochemistry 235, p. 1001-107 (1998)).

b) TaqMan Hybridization Probes

A single-stranded hybridization probe is labelled with two components.When the first component is excited with light of a suitable wavelength,the absorbed energy is transferred to the second component, theso-called quencher, according to the principle of fluorescence resonanceenergy transfer. During the annealing step of the PCR reaction, thehybridization probe binds to the target DNA and is degraded by the 5′-3′exonuclease activity of the Taq polymerase during the subsequentelongation phase. As a result the excited fluorescent component and thequencher are spatially separated from one another and thus afluorescence emission of the first component can be measured.

c) Molecular Beacons

These hybridization probes are also labelled with a first component andwith a quencher, the labels preferably being located at both ends of theprobe. As a result of the secondary structure of the probe, bothcomponents are in spatial proximity in solution. After hybridization tothe target nucleic acid both components are separated from one anothersuch that after excitation with light of a suitable wavelength thefluorescence emission of the first component can be measured (Lizardi etal., U.S. Pat. No. 5,118,801).

In the described embodiments in which only the target nucleic acid oronly the reference nucleic acid or an external standard is amplified inone reaction vessel in each case, the respective amplification productcan also be detected according to the invention by a DNA binding dyewhich emits a corresponding fluorescence signal upon interaction withthe double-stranded nucleic acid after excitation with light of asuitable wavelength. The dyes SybrGreen and SybrGold (Molecular Probes)have proven to be particularly suitable for this application.Intercalating dyes can alternatively be used.

A subject matter of the invention are also kits that contain appropriateagents to carry out the method according to the invention. According tothe invention these agents are present in the kit in variouscompositions. A kit preferably contains reagents such as for example areverse transcriptase for preparing a cDNA, DNA polymerase for theamplification reaction, specific primers for the amplification reactionand optionally also specific hybridization probes to detect theamplification product. As an alternative polymerases for a single-stepRT-PCR reaction can be present in the kit. It is also possible that akit according to the invention contains package inserts or diskscontaining files with previously determined amplification efficienciesfor defined amplification conditions. Finally the invention alsoconcerns a kit which additionally contains further reagents for thesynthesis and labelling of oligonucleotides such as fluorescentNHS-esters or fluorescent-labelled CPGs. Moreover a kit according to theinvention can optionally also contain a DNA which can be used as aninternal or external standard.

EXAMPLES

The invention is further elucidated by the following examples:

Example 1 Amplification of Cytokeratin 20 (CK20) and Porphobilinogen(PBGD) cDNAs

RNA was isolated from the cell line HT-29 (ATCC) using a HighPure-RNARestriction Kit (Roche Diagnostics GmbH). After semi-quantitativespectrophotometric determination, the RNA concentration was adjusted to100 ng/μl in RNA-free water. Three serial single dilutions were preparedfrom this with RNA concentrations of 10 ng, 1 ng and 100 pg/μl.

Total cDNA was prepared from these dilutions by reverse transcriptionunder the following conditions:

1 x AMV reverse transcription buffer 1 mM of each deoxynucleosidetriphosphate 0.0625 mM randomized hexamers

10 u AMV reverse transcriptase 10 μl RNA Ad. 20 μl water

All mixtures were incubated for 10 minutes at 25° C., 30 minutes at 42°C. and 5 minutes at 95° C. for the cDNA synthesis. Subsequently theywere cooled to 4° C. A sample containing 10 ng/μl HT29 RNA was used as acalibrator.

Afterwards the amplification reaction was carried out which was measuredin real-time in the FRET HybProbe format on a LightCycler instrument(Roche Diagnostics GmbH). Each reaction mixture was amplified under thefollowing conditions:

1 x fast start DNA hybridization probes buffer 1 x detection mix 2 μlcDNA Ad. 20 μl water

The 1× detection mix was composed of 0.5 μM forward and 0.5 μM reverseprimers, each, 0.2 μM fluorescein and LC-Red 640 labelled hybridizationprobes, 4 mM magnesium chloride and 0.005% Brij-35.

Primers having SEQ ID NO:1 and SEQ ID NO:2 were used to amplify a CK20sequence. The CK20 product was detected using a fluorescein probe havingSEQ ID NO:3 and a LC-Red 640 hybridization probe having SEQ ID NO:4.Primers having SEQ ID NO:5 and 6 were used to detect the PBGD sequence.PBGD was detected using a fluorescein-labelled hybridization probehaving SEQ ID NO:7 and an LC-Red 640-labelled hybridization probe havingSEQ ID NO:8.

The reaction mixtures were firstly incubated for 10 minutes at 95° C. inthe presence of 5 mM magnesium chloride for the amplification. Theactual amplification reaction was carried out for 50 cycles according tothe following scheme:

-   10 sec. 95° C.-   10 sec. 60° C.-   5 sec. 72° C.

After each incubation at 60° C. a fluorescence measurement was carriedout according to the manufacturer's instructions. The Cp value wasdetermined as the maximum of the 2^(nd) derivative of the amplificationreaction as a function of the cycle number.

Example 2 Determination of the Efficiency of the Amplification of CK20and PBGD

A function was established to determine the efficiency in which thecycle number Cp determined for the respective concentration wasdetermined as a function of the decadic logarithm of the RNAconcentration used.

A linear function was calculated from this function by regressionanalysis with the aid of the LightCycler software. Starting from thisfunction the efficiency was determined according to the equationefficiency=10^(−1/a)wherein ^(a) is the gradient (1^(st) derivative) of the determinedregression line.

TABLE 2 Conc (ng) Log (ng) Cp-CK20 Cp-PBGD   0.1 −1.0 35.73 38.73 1 0.030.13 33.59  10 1.0 24.20 28.63 Efficiency: 1.491 1.578 Cp: measuredcycle number

The results obtained for CK20 and PBGD are shown in Table 2. The resultshows that on the one hand the efficiencies are considerably differentfrom 2.00 i.e. a doubling of the target nucleic acid does not take placewith each PCR cycle. On the other hand, the result shows that theefficiencies of the amplification of CK20 and PBGD differ significantlyfrom one another under otherwise identical conditions.

Example 3 Determination of the Original Ratio of Target Nucleic Acid andReference Nucleic Acid with and without Correction of the AmplificationEfficiency

Under the conditions described in Example 1 the ratio determined of theoriginal amount of CK20 and PBGD should be independent of the respectiveamplified concentration of the sample material used. Hence thedetermination of the ratio for various amounts of sample RNA was used tocheck the effect of an efficiency correction on the basis of themeasured values that were obtained. In this case the ratio of CK20 toPBGD was determined according to the invention according to equation(5). On the one hand, the ratio was determined using the efficienciesobtained from example 2 and on the other hand with an assumedamplification efficiency of 2.00 for CK20 and for PGD. The results areshown in Table 3:

TABLE 3 N(T)₀/N(R)₀ HT29 CP Cp N(T)₀/N(R)₀ Efficiency (ng) CK20 PBGDEfficiency = 2 corrected 0.1 ng 35.73 38.73 8.00 29.68   1 ng 30.1333.59 11.00 26.66  10 ng 24.20 28.63 21.56 29.66 M: 13.52 28.66 SD: 7.121.74 % CV: 52.7% 6.1% Cp = measured cycle number M = mean SD = standarddeviation % CV = coefficient of variation

As can be seen from the table, the efficiency-corrected valuescalculated for the ratio of N(T)₀/N(R)₀ have a significantly lowerstandard deviation for the various amounts of sample RNA than theuncorrected values and a coefficient of variation of 6.1% compared to52.7%.

Example 4 Efficiency-correction when Using a Calibrator

Analogously to Examples 1 and 2 amplification reactions were carried outin the presence of 10 mM magnesium chloride. In this case an efficiencyof 1.491 was determined for CK20 and an efficiency of 1.578 wasdetermined for PBGD. In addition the Cp values of a calibrator samplecontaining an unknown amount of HT-29 RNA was determined at 5 mM and 10mM magnesium chloride. The measured data were used to determine thequotients of the ratios of CK20 to PBGD between the samples analysed ineach case and the appropriate calibrator according to equation (7). Thisdetermination was carried out on the one hand with an assumed efficiencyof 2 for the amplification of CK20 and PBGD as well as, on the otherhand, with the aid of experimentally determined amplificationefficiencies. The result is shown in Table 4.

TABLE 4 T:R/C HT29 Cp Cp T:R/C Efficiency MgCl₂ (ng) CK20 PBGDEfficiency corrected  5 mM 0.1 ng 36.59 39.09 0.76 0.92  5 mM 1 ng 30.6032.60 0.54 0.72  5 mM 10 ng 25.19 27.95 0.91 0.95 calibrator Cal. 24.7827.67 1.00 1.00 10 mM 0.1 ng 35.73 38.73 0.39 1.04 10 mM 1 ng 30.1333.59 0.53 0.93 10 mM 10 ng 24.20 28.63 1.04 1.04 calibrator Cal. 24.0128.38 1.00 1.00 M: 0.70 0.93 SD: 0.26 0.10 % CV: 36.7% 11.1%${T\text{:}R\text{/}C} = {\frac{{N(T)}_{0A}}{{N(R)}_{0A}}/\frac{{N(T)}_{0K}}{{N(R)}_{0K}}}$Cp = measured cycle number M = mean SD = standard deviation % CV =coefficient of variation

As can be seen in Table 4, the efficiency-corrected values have a lowerstandard deviation (0.10) as well as a three-fold lower coefficient ofvariation than the T:R/C values with an assumed PCR efficiency of 2.00.This result shows that an efficiency correction according to theinvention is also advantageous in quantifications in which astandardization with the aid of calibrators has already been carriedout.

Example 5 Absolute Quantification of Plasmid DNA

A decadic dilution series of a plasmid containing the PSA gene of 10⁹ to10² copies was prepared for this purpose. At the same time a seconddecadic dilution series with a plasmid containing the gene for TNF(tumour necrosis factor) with an unknown copy number of plasmid DNA wasprepared. Afterwards the PSA reaction mixtures were amplified on aLightCycler (Roche Diagnostics) under standard conditions using theprimers having SEQ ID NO:9 and 10 and the TNF reaction mixtures wereamplified using the primers having SEQ ID NO: 11 and 12 (RocheDiagnostics LightCycler SybrGreen Mastermix, 5 mM final concentrationMgCl₂, 0.5 μM final concentration of each primer). The amplification wasmeasured in real-time using the DNA binding agent SybrGreenI (MolecularProbes) under standard conditions in which the evaluation was carriedout according to the manufacturer's instructions in the secondderivative mode.

The original copy number of the TNF plasmid was determined in twodifferent ways on the basis of the obtained data.

On the one hand a calibration line based on the PSA amplification wasgenerated assuming the same amplification efficiency for PSA and TNF.

On the other hand the original copy number was determined according toformula (8). Analogously to example 2 the amplification efficiency forPSA and TNF was determined by calculating a regression line according tothe formulaE=10^(−1/a)wherein ^(a) denotes the increase (1^(st) derivative) of the calculatedregression line. In this case an amplification efficiency of 2.03 wasdetermined for PSA and an amplification efficiency of 2.13 wasdetermined for TNF.

The results of the two different quantification procedures are shown inTable 5. A so-called dilution check was carried out as a measure for theaccuracy of the determination. The values denoted dilution check arecalculated from the quotients of the copy numbers measured for therespective dilution of two dilution mixtures that differ from oneanother by a factor of 10. Thus a value of 10.00 would be expected asthe ideal value.

TABLE 5 Not efficiency corrected Efficiency corrected DeterminedDetermined copy number copy number per Dilution Dilution per dilutionDilution check dilution check  1 30826128 10.10 27728632 12.12 10⁻¹3053000 13.82 2287050 14.98 10⁻² 220900 7.19 152643 7.94 10⁻³ 3071011.61 19227 13.89 10⁻⁴ 2646 8.55 1384 9.52 10⁻⁵ 309.5 7.61 145.4 8.7610⁻⁶ 40.66 3.86 16.6 3.84 10⁻⁷ 10.54 4.3 Mean: 8.96 10.16

As the result of the dilution check from Table 5 shows, the mean of theefficiency-corrected data results in a value of 10.16, whereas the meanof non-efficiency-corrected data results in a value of 8.96 which isconsiderably further away from the ideal value of 10.00. From this itfollows that an efficiency correction is also advantageous forembodiments in which an absolute quantification of nucleic acids withthe aid of PCR is carried out.

The present invention is not to be limited in scope by the exemplifiedembodiments which are intended as illustrations of single aspects of theinvention. Various modifications of the invention in addition to thosedescribed herein will become apparent to those skilled in the art fromthe foregoing description and accompanying drawings. Such modificationsare intended to fall within the scope of the appended claims. Allpublications cited herein are incorporated by reference in theirentirety.

1. A method for the quantification of a target nucleic acid in a testsample relative to a reference nucleic acid by using a calibratorsample, wherein the calibrator sample comprises the target nucleic acidand the reference nucleic acid and the test sample comprises the targetnucleic acid and the reference nucleic acid, comprising: a) determiningamplification efficiencies of the target nucleic acid and of thereference nucleic acid under defined amplification conditions, b)amplifying the target nucleic acid contained in the test sample and thereference nucleic acid contained in the test sample under the samedefined reaction conditions, c) measuring the amplification of thetarget nucleic acid from the test sample and of the reference nucleicacid from the test sample in real time to determine amplified amounts ofthe target nucleic acid and the reference nucleic acid from the testsample, d) amplifying the target nucleic acid contained in a calibratorsample and the reference nucleic acid contained in the calibrator sampleunder the same defined reaction conditions, e) measuring theamplification of the target nucleic acid from the calibrator sample andof the reference nucleic acid from the calibrator sample in real time todetermine amplified amounts of the target nucleic acid and the referencenucleic acid from the calibrator sample, and f) combining the amplifiedamounts determined for the sample and for the calibrator sample in stepsc) and e) with the aid of the amplification efficiencies determined instep a), wherein the combining is based upon the formula${\frac{{N(T)}_{0A}}{{N(R)}_{0A}}/\frac{{N(T)}_{0K}}{{N(R)}_{0K}}} = {{E(R)}^{{{nA}{(R)}} - {{nK}{(R)}}}*{E(T)}^{{{nK}{(T)}} - {{nA}{(T)}}}}$, wherein N(T)_(0i)=the original amount of target DNA presentN(R)_(0i)=the original amount of reference DNA present E(R)=theamplification efficiency of the reference nucleic acid ni(R)=the cyclenumber of the reference nucleic acid E(T)=the amplification efficiencyof the target nucleic acid ni(T)=the cycle number of the target nucleicacid and i=A are values of the test sample and i=K are values of thecalibrator sample, g) determining a measure for the original amount oftarget nucleic acid in the sample using the formula in step f).
 2. Themethod of claim 1, wherein the efficiency of the amplification isdetermined by a) preparing a dilution series of the target nucleic acidand the reference nucleic acid, b) amplifying the target nucleic acidand the reference nucleic acid under defined reaction conditions asclaimed in claim 1, the amplification of the nucleic acid being measuredin real time, c) determining a defined threshold value, d) determiningthe cycle number at which the signal threshold value is exceeded foreach dilution, e) determining a logarithmic linear function of the copynumber of target nucleic acid and reference nucleic acid used for theamplification as a function of the cycle number at which the signalthreshold value is exceeded and f) calculating the amplificationefficiency E according toE=G^(−a), wherein ^(a) is determined as the first derivative of thefunction determined in step e) and G is the base number of thelogarithm.
 3. The method of claim 1, wherein the efficiency of theamplification is determined by a) preparing a dilution series of thetarget nucleic acid and the reference nucleic acid, b) amplifying thetarget nucleic acid and the reference nucleic acid under definedreaction conditions as claimed in claim 1, the amplification of thenucleic acid being measured in real time, c) determining a definedsignal threshold value, d) determining the cycle number at which thesignal threshold value is exceeded for each dilution, e) determining alinear function of the cycle number determined in step d) as a functionof a logarithm of the copy number of target nucleic acid and thereference nucleic acid used for the amplification and f) calculating theamplification efficiency E according toE=G^(−1/a), wherein ^(a) is determined as the first derivative of thefunction determined in step e) and G is the base number of thelogarithm.